{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\sum_{i=0}^n i^2 = \\frac{(n^2+n)(2n+1)}{6}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$f(x,y,z)=3y^2z\\left(3+\\frac{7x+5}{1+y^2}\\right)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\left. \\frac{{\\rm d}u}{{\\rm d}x} \\right| _{x=0}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ \\frac{a+1}{b+1} \\quad and \\quad {a+1 \\over b+1}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\sqrt{2} \\quad and \\quad \\sqrt[n]{3}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$f(x_1, x_2, \\ldots, x_n)=x_1^2+x_2^2+\\cdots+x_n^2$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\vec{a} \\cdot \\vec{b} = 0$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\overleftarrow{xy} \\quad and \\quad \\overleftrightarrow{xy} \\quad and \\quad \\overrightarrow{xy}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$xy \\text{ with arrows: } \\quad \\overleftarrow{xy} \\; \\mid \\; \\overleftrightarrow{xy} \\; \\mid \\; \\overrightarrow{xy}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ \\int_0^1 {x^2} \\, {\\rm d}x$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ \\lim_{n \\to +\\infty} \\frac{1}{n(n+1)} \\quad and \\quad lim_{x \\leftarrow{示例}} \\frac{1}{n(n+1)}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\sum_{i=1}^n \\frac{1}{i^2} \\quad \\prod_{i=1}^n \\frac{1}{i^2} \\quad \\bigcup_{i=1}^2 R$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\n",
    "\\begin{matrix}\n",
    "1 & x & x^2 \\\\\n",
    "1 & y & y^2 \\\\\n",
    "1 & z & z^2\n",
    "\\end{matrix}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\n",
    "\\begin{pmatrix}\n",
    "1 & x & x^2 \\\\\n",
    "1 & y & y^2 \\\\\n",
    "1 & z & z^2 \n",
    "\\end{pmatrix}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\n",
    "\\begin{bmatrix}\n",
    "1 & x & x^2 \\\\\n",
    "1 & y & y^2 \\\\\n",
    "1 & z & z^2\n",
    "\\end{bmatrix}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\n",
    "\\begin{Bmatrix}\n",
    "1 & x & x^2 \\\\\n",
    "1 & y & y^2 \\\\\n",
    "1 & z & z^2\n",
    "\\end{Bmatrix}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\n",
    "\\begin{vmatrix}\n",
    "1 & x & x^2 \\\\\n",
    "1 & y & y^2 \\\\\n",
    "1 & z & z^2\n",
    "\\end{vmatrix}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\n",
    "\\begin{Vmatrix}\n",
    "1 & x & x^2 \\\\\n",
    "1 & y & y^2 \\\\\n",
    "1 & z & z^2\n",
    "\\end{Vmatrix}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\n",
    "\\begin{pmatrix}\n",
    "1 & a_1 & a_1^2 & \\cdots & a_1^n \\\\\n",
    "1 & a_2 & a_2^2 & \\cdots & a_2^n \\\\\n",
    "\\vdots & \\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
    "1 & a_n & a_n^2 & \\cdots & a_n^n\n",
    "\\end{pmatrix}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\n",
    "\\left[\n",
    "    \\begin{array}{cc|c}\n",
    "        1 & 2 & 3 \\\\\n",
    "        4 & 5 & 6\n",
    "    \\end{array}\n",
    "\\right]\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\n",
    "\\bigl(\n",
    "    \\begin{smallmatrix}\n",
    "        1 & 2 \\\\\n",
    "        3 & 4\n",
    "    \\end{smallmatrix}\n",
    "\\bigr)\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\n",
    "\\left\\{\n",
    "    \\begin{array}{c}\n",
    "        a_1 x + b_1 y + c_1 z = d_1 \\\\\n",
    "        a_2 x + b_2 y + c_2 z = d_2 \\\\\n",
    "        a_3 x + b_3 y + c_3 z = d_3\n",
    "    \\end{array}\n",
    "\\right.\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\n",
    "\\begin{align}\n",
    "    v + w & = 0 & \\text{Given} \\tag 1\\\\\n",
    "    -2 & = -w + 0 & \\text{additive identity} \\tag 2\\\\\n",
    "    -2 + 0 & = -2 + (v + w) & \\text{equations (1) and (2)} \\tag 3\\\\\n",
    "\\end{align}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\n",
    "f(n) = \n",
    "\\begin{cases}\n",
    "    n/2, & \\text{if n is even} \\\\\n",
    "    3n+1, & \\text{if n is odd}\n",
    "\\end{cases}\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "f(n) = \n",
    "\\begin{cases}\n",
    "    \\frac{n}{2} & \\text{if $n$ is even} \\\\\n",
    "    3n + 1 & \\text{if $n$ is odd}\n",
    "\\end{cases}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\n",
    "\\begin{array}{c|lcr}\n",
    "    n & \\text{左对齐} & \\text{居中对齐} & \\text{右对齐} \\\\\n",
    "    \\hline\n",
    "    1 & 0.24 & 1 & 125 \\\\\n",
    "    2 & -1 & 189 & -8 \\\\\n",
    "    3 & -20 & 2000 & 1 + 10i\n",
    "\\end{array}\n",
    "$"
   ]
  }
 ],
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